https://doi.org/10.1007/s100510050123
Born effective charge reversal and metallic threshold state at a band insulator-Mott insulator transition
1
International School for Advanced Studies (SISSA),
Via Beirut 2-4, 34014 Trieste, Italy
2
Istituto Nazionale di Fisica della Materia (INFM), Unita' Trieste
SISSA, 34014 Trieste, Italy
3
International Centre for Theoretical Physics, P.O. Box 586, 34014
Trieste, Italy
Received:
21
May
1999
Published online: 15 March 2000
We study the quantum phase transition between a band ("ionic")
insulator and a Mott-Hubbard insulator, realized at a critical value
in a bipartite Hubbard model with two inequivalent sites,
whose on-site energies differ by an offset Δ.
The study is carried out both in D=1 and D=2 (square and honeycomb
lattices), using exact Lanczos diagonalization, finite-size scaling, and
Berry's phase calculations of the polarization. The Born effective
charge jump from positive infinity to negative infinity
previously discovered in D=1 by Resta and Sorella
is confirmed to be directly connected with the transition from the band
insulator to the Mott insulating state, in agreement
with recent work of Ortiz et al. In addition, symmetry is
analysed, and the transition is found to be associated with a
reversal of inversion symmetry in the ground state, of
magnetic origin. We also study the D=1 excitation spectrum
by Lanczos diagonalization and finite-size scaling. Not only
the spin gap closes at the transition,
consistent with the magnetic nature of the Mott state, but also
the charge gap closes, so that the intermediate state
between the two insulators appears to be metallic.
This finding, rationalized within
Hartree-Fock as due to a sign change of the effective on-site energy
offset Δ for the minority spin electrons, underlines the
profound difference between the two
insulators. The band-to-Mott insulator transition is also studied
and found in the same model in D=2. There too we find an associated,
although weaker,
polarization anomaly,
with some differences between square and honeycomb lattices.
The honeycomb lattice, which does not possess an inversion symmetry,
is used to demonstrate the possibility of an inverted piezoelectric
effect in this kind of ionic Mott insulator.
PACS: 75.10.Jm – Quantized spin models / 71.20.-b – Electron density of states and band structure of crystalline solids / 71.27.+a – Strongly correlated electron systems; heavy fermions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000